See that screenshot. It certainly shows you when your 5 hour session is set to refresh, in my understanding it also attempts to show you how you're doing with other limits via projection.
It's not exactly the same thing, but imagine my complete surprise when, in the middle of a discussion with Copilot and without warning, it announced that the conversation had reached its length limit and I had to start a new one with absolutely no context from the current one. Copilot has many, many usability quirks, but that was the first that actually made me mad.
ChatGPT and Claude do the same. And I have noticed that model performance can often degrade a lot before such a hard limit. So even when not hitting the hard limit, splitting out to a new session can be useful.
Context management is the new prompt engineering...